I have seen many times in small drones that sometimes the battery warning signal activates itself long before the battery needs to be charged. Upon checking the voltage, I find that it´s near to 3.8, 3.9 and sometimes even 4.0 volts. The same drone sometimes "decides" to work and warn you when the battery reaches 3.6 or 3.7v. I used to think that when the temperature was lower these errors might occur, but the temperature drop was just a few degrees (discarding this option).

I heard about quite a lot of cases in which a similiar thing also happened to Phantoms, and I would like to know if anybody has a clue to what's going on.

There are settings in the DJI go app where you can change the battery level on which the app will warn you that it is low.

Smart Battery. It  calculates based on your rate of consumption and such. Simple example, the first 5 minutes of flight you have strong headwinds and consume 50%, then fly down wind back, you use only 10% and it only took 2 minutes. The battery will the information and average the consumption to get its %.  Just a crude, example there many things that are factored in.
EDIT: That’s also why you should not start with a partly changed battery. Once it’s turned off it’s going to start calculating as if it’s fully charged when turned back on.  That’s why you see post saying “ my battery dropped from 50% to 10% in 2 minutes”.

Might be so with smart batteries... But any ideas about dumb ones?

Calculating current consumption and predicting the future probably relies on a PID system. If you could alter the constant which makes the past consumption so important to the future one, you might solve that issue. But that would involve hacking DJI soft and hardware, so not good idea